Locate each of the isolated singularities of the given function and tell whether it is a removable singularity, a pole, or an essential singularity. If the singularity is removable, give the vlaue of the function at the point; if the singularity is a pole, give the order of the pole.

(1)

(2)

(3)

If anyone could show me how to do any of these, I would appreciate it. I don't understand it..Thanks!

October 9th 2008, 03:10 PM

shawsend

(1) If is a removable singularity, then right?

So .

(2) If has a pole of order then with . The numerator of the second one is zero at z=1. So it's not as simple as it looks. Need to factor the numerator:

. That just looks like a removable singularity right but we could check that by (1) above:

The third one has a pole of order 1 at z=-2 by (2).

October 9th 2008, 03:15 PM

mr fantastic

Quote:

Originally Posted by shadow_2145

Locate each of the isolated singularities of the given function and tell whether it is a removable singularity, a pole, or an essential singularity. If the singularity is removable, give the vlaue of the function at the point; if the singularity is a pole, give the order of the pole.